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Unformatted text preview: HW#5 SolutionGuide-- Using Matlab REMARK: We will discuss this in class, specially problem 6 for the Eigenvalues/vectors of B. As the eigenvalues of B are Lambda1=(15+(297)^0.5)/2, Lambda2==(15- (297)^0.5)/2, and Lambda3=0. It you use approximation of the first 2 eigenvalues, you would get numerical errors and NO (non-zero) eigenvector can be obtained. This simple matrix shows that careful use of any computational software (including MATLAB) has to be applied as a supportive tool, not an end of/to itself. For the purpose of grading, we shall not penalize you. However, this is a challenging problem that illustrates the need to be careful in applying these software tools. ____ Given X1=[1 2 3]' X1 = 1 2 3 X2=[4 5 6]' X2 = 4 5 6 X3=[7 8 9]' X3 = 7 8 9 B=[X1 X2 X3] B = 1 4 7 2 5 8 3 6 9 rank(B) ans = 2 poly(B) ans = 1.0000 -15.0000 -18.0000 -0.0000 %This computes the coefficients of the characteristic polynomial of the matrix B as in %det(Lambda*I-B)=0. A=[1 3;2 4] A = 1 3 2 4 rank(A) ans = 2 1) %Rank of a matrix-- Use Row-reduced Row Echelon Form REF A A = 1 3 2 4 %Apply the reduction to the Identity matrix and pre-multiply it to A at every step....
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